If the tests above are good, Apply 10Vpp at 1kHz to Pin 1 with Pin 3 connected to the generator ground

Measure V from Pin 2 to Pin 3 using the same ground point (should be about 5Vpp)

Measure V from Pin 4 to Pin 5 (should be about 9.8Vpp)

Measure V from Pin 6 to Pin 7 (should be about 9.8Vpp)

NOTE: A bad cable can make a circuit act as if the transformer has failed.
If you are having strange problems with your transformer...

check your cables to make sure that they all have good grounds

The scope Ch1, CH2, and function generator all have a common ground.
The common ground can hide a bad cable ground because the other cables provide a ground path.
The ground connection fails when you go through a transformer because the primary and secondary windings are isolated from each other.
If you seem to have a signal on the secondary until you connect all of the cable grounds, one of the cables is bad.

The ohm meter can check for a broken ground in a cable.

If the bad connection is intermittent, it can be very difficult to find.